cp's OEIS Frontend

A339117 Number of cycles in the grid graph P_5 X P_n.

%I A339117 #17 Feb 16 2025 08:34:01
%S A339117 10,108,1049,9349,80626,692194,5948291,51139577,439673502,3779989098,
%T A339117 32497334055,279386435639,2401945965628,20650054358200,
%U A339117 177533025653767,1526290165248783,13121849649571820,112811405309454694,969864273118112913,8338134834111643373,71684765011673779732
%N A339117 Number of cycles in the grid graph P_5 X P_n.
%C A339117 a(n+1) / a(n) tends to 8.597218255461742020947886618374491114891840151635008721734194641555448999... - _Vaclav Kotesovec_, Nov 24 2020
%H A339117 Seiichi Manyama, <a href="/A339117/b339117.txt">Table of n, a(n) for n = 2..500</a>
%H A339117 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GraphCycle.html">Graph Cycle</a>
%H A339117 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GridGraph.html">Grid Graph</a>
%F A339117 Empirical g.f.: -x^2*(10 - 42*x + 149*x^2 - 300*x^3 - 393*x^4 + 693*x^5 + 230*x^6 - 473*x^7 - 72*x^8 + 202*x^9 + 84*x^10) / ((1 - x)^2 * (-1 + 13*x - 45*x^2 + 66*x^3 - 17*x^4 - 209*x^5 + 151*x^6 + 140*x^7 - 112*x^8 - 48*x^9 + 50*x^10 + 28*x^11)). - _Vaclav Kotesovec_, Nov 24 2020
%o A339117 (Python)
%o A339117 # Using graphillion
%o A339117 from graphillion import GraphSet
%o A339117 import graphillion.tutorial as tl
%o A339117 def A(n, k):
%o A339117     universe = tl.grid(n - 1, k - 1)
%o A339117     GraphSet.set_universe(universe)
%o A339117     cycles = GraphSet.cycles()
%o A339117     return cycles.len()
%o A339117 def A339117(n):
%o A339117     return A(n, 5)
%o A339117 print([A339117(n) for n in range(2, 15)])
%Y A339117 Cf. A140517, A231829.
%K A339117 nonn
%O A339117 2,1
%A A339117 _Seiichi Manyama_, Nov 24 2020